The biggest similarity would be that they were old empires / kingdoms / dynasties (originating from the Middle Ages, sort of) that eventually caved to modern nation-states military might and conquest, particularly the British and Germans. Both the Ottoman and Qing were very dominant during its heyday, and ruled over many subjects covering lots of ground. But then their old traditions and outdated military got overpowered by Western post-industrial war machines at the turn of the 20th century.

The major difference would be that the Ottoman empire was a theocracy, a religion-based form of government, ruled by a caliphate and with laws derived from their holy scriptures, aka the Qur'an. Whereas, with the Qing dynasty, on its surface they were secular, although it's arguable that their philosophical-political system of government, Confucianism, has significant religiosity also.

Ultimately, both collapsed as victims of the a globalized chaos that emerged for the first time in history, of that magnitude, with belligerent rulers of the nation-state aspiring to conquer all, aka World War I.